On the basis of a cognitive linguistics approach, namely that linguistic semantics corresponds to conceptual structures and that semantic representations should therefore reflect conceptual configurations, this paper discusses the adequate representation of conceptual relations that can be found in the semantic structure of verbs. As representational framework, a unique modelling language for linguistic semantics - the Unified Eventity Representation (UER) - is deployed. The UER is unprecedented in that it is based on the object-oriented and graphical Unified Modeling Language (UML) from computer science. We describe prominent characteristics of the UER, outline the types of conceptual relations and how they are represented in the UER, and conclude with an assessment of the modelling power of the UER with respect to the representation of conceptual relations.